My best guess, and this is only a guess, would be that it's a maple tree. In the second picture, to the right of your ear, there's a scale of bark separating from the top side that looks thin (which can make climbing hard). When a scale of maple bark separates it can be relatively thin like that, whereas other common trees, oak or walnut, usually have thicker, bark that doesn't scale as much. On the flip side, it doesn't look as scaly as I would expect from say cherry.
chambers1589